Quantum field theory and pair creation/annihilation

The creation and annihilation of matter-antimatter pairs is usually taken as proof that, somehow, fields can condense into matter-particles or, conversely, that matter-particles can somehow turn into light-particles (photons), which are nothing but traveling electromagnetic fields. However, pair creation always requires the presence of another particle and one may, therefore, legitimately wonder whether the electron and positron were not already present, somehow.

Carl Anderson’s original discovery of the positron involved cosmic rays hitting atmospheric molecules, a process which involves the creation of unstable particles including pions. Cosmic rays themselves are, unlike what the name suggests, no rays – not like gamma rays, at least – but highly energetic protons and atomic nuclei. Hence, they consist of matter-particles, not of photons. The creation of electron-positron pairs from cosmic rays also involves pions as intermediate particles:

1. The π+ and π particles have net positive and negative charge of 1 e+ and 1 e respectively. According to mainstream theory, this is because they combine a u and d quark but – abandoning the quark hypothesis[1] – we may want to think their charge could be explained, perhaps, by the presence of an electron![2]

2. The neutral pion, in turn, might, perhaps, consist of an electron and a positron, which should annihilate but take some time to do so!

Neutral pions have a much shorter lifetime – in the order of 10-18 s only – than π+ and π particles, whose lifetime is a much more respectable 2.6 times 10-8 s. Something you can effectively measure, in order words.[3] In short, despite similar energies, neutral pions do not seem to have a lot in common with π+ and π particles. Even the energy difference is quite substantial when measured in terms of the electron mass: the neutral pion has an energy of about 135 MeV, while π+ and π particles have an energy of almost 140 MeV. To be precise, the difference is about 4.6 MeV. That is quite a lot: the electron rest energy is 0.511 MeV only.[4] So it is not stupid to think that π+ and π particles might carry an extra positron or electron, somehow. In our not-so-humble view, this is as legitimate as thinking – like Rutherford did – that a neutron should, somehow, combine a proton and an electron.[5]

The whole analysis – both in the QED as well as in the QCD sector of quantum physics – would radically alter when thinking of neutral particles – such as neutrons and π0 particles – not as consisting of quarks but of protons/antiprotons and/or electrons/positrons cancelling each other’s charges out. We have not seen much – if anything – which convinces us this cannot be correct. We, therefore, believe a more realist interpretation of quantum physics should be possible for high-energy phenomena as well. With a more realist theory, we mean one that does not involve quantum field and/or renormalization theory.

Such new theory would not be contradictory to the principle that, in Nature, the number of charged particles is no longer conserved, but that total (net) charge is actually being conserved, always. Hence, charged particles could appear and disappear, but they would be part of neutral particles. All particles in such processes are very short-lived anyway, so what is a particle here? We should probably think of these things as an unstable combination of various bits and bobs, isn’t it? 😊

So, yes, we did a paper on this. And we like it. Have a look: it’s on ResearchGate, academia.edu, and – as usual – Phil Gibb’s site (which has all of our papers, including our very early ones, which you might want to take with a pinch of salt). 🙂


[1] You may be so familiar with quarks that you do not want to question this hypothesis anymore. If so, let me ask you: where do the quarks go when a π± particle disintegrates into a muon-e±?

[2] They disintegrate into muons (muon-electrons or muon-positrons), which themselves then decay into an electron or a positron respectively.

[3] The point estimate of the lifetime of a neutral pion of the Particle Data Group (PDG) is about 8.5 times 10-17 s. Such short lifetimes cannot measured in a classical sense: such particles are usually referred to as resonances (rather than particles) and the lifetime is calculated from a so-called resonance width. We may discuss this approach in more detail later.

[4] Of course, it is much smaller when compared to the proton (rest) energy, which it is about 938 MeV.

[5] See our short history of quantum-mechanical ideas or our paper on protons and neutrons.

2 thoughts on “Quantum field theory and pair creation/annihilation

  1. Jean: I’m sure gamma gamma pair production is very simple. When two 511keV photons interact to create an electron and a positron, their paths change from linear paths to closed paths. The opposite happens in electron-positron annihilation. Both de Broglie and Schrodinger talked about waves in a closed path in the 1920s. Look to TQFT and say an electron is a “trivial knot” whilst a proton is a trefoil knot, See the trefoil picture here https://physicsdetective.com/wp-content/uploads/protontrefoil1.png. Trace around the trefoil anticlockwise from the bottom left calling out the crossing-over directions: up down up. .

    1. Thanks ! That looks nice. I guess the next challenge in such ‘closed loop’ theories is to work out the equations of motion for Rutherford’s ‘nuclear electron’ (the neutron consisting of a proton and an electron – with the electron acting as the ‘glue’ between the protons). That would be a nice ‘realist’ theory of the fundamental structure of nuclei !

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